Laser Ablation Molecular Isotopic Spectrometry: Strontium and its isotopes

The experimental details are reported of Laser Ablation Molecular Isotopic Spectrometry (LAMIS) and its application for performing optical isotopic analysis of solid strontium-containing samples in ambient atmospheric air at normal pressure. The LAMIS detection method is described for strontium isotopes from samples of various chemical and isotopic compositions. The results demonstrate spectrally resolved measurements of the three individual ⁸⁶Sr, ⁸⁷Sr, and ⁸⁸Sr isotopes that are quantified using multivariate calibration of spectra. The observed isotopic shifts are consistent with those calculated theoretically. The measured spectra of diatomic oxide and halides of strontium generated in laser ablation plasmas demonstrate the isotopic resolution and capability of LAMIS. In particular, emission spectra of SrO and SrF molecular radicals provided clean and well resolved spectral signatures for the naturally occurring strontium isotopes. A possibility is discussed of using LAMIS of strontium isotopes for radiogenic age determination.     

Integral equation formulation for buoyancy-driven convection problems

An integral equation formulation for buoyancy-driven convection problems is developed and illustrated. Buoyancy-driven convection in a bounded cylindrical geometry with a free surface is studied for a range of aspect ratios and Nusselt numbers. The critical Rayleigh number, the nature of the cellular motion, and the heat transfer enhancement are computed using linear theory. Green's functions are used to convert the linear problem into linear Fredholm integral equations. Theorems are proved which establish the properties of the eigenvalues and eigenfunctions of the linear integral operator which appears in these equations.     

Local entropy and structure in a two-dimensional frustrated system

We calculate the local contributions to the Shannon entropy and excess entropy and use these information theoretic measures as quantitative probes of the order arising from quenched disorder in the diluted Ising antiferromagnet on a triangular lattice. When one sublattice is sufficiently diluted, the system undergoes a temperature-driven phase transition, with the other two sublattices developing magnetizations of equal magnitude and opposite sign as the system is cooled.(1) The diluted sublattice has no net magnetization but exhibits spin glass ordering. The distribution of local entropies shows a dramatic broadening at low temperatures; this indicates that the system's total entropy is not shared equally across the lattice. The entropy contributions from some regions exhibit local reentrance, although the entropy of the system decreases monotonically as expected. The average excess entropy shows a sharp peak at the critical temperature, showing that the excess entropy is sensitive to the structural changes that occur as a result of the spin glass ordering.     

Isomorph-Free Exhaustive Generation

We describe a very general technique for generating families of combinatorial objects without isomorphs. It applies to almost any class of objects for which an inductive construction process exists. In one form of our technique, no explicit isomorphism testing is required. In the other form, isomorph testing is restricted to within small subsets of the entire set of objects. A variety of different examples are presented, including the generation of graphs with some hereditary property, the generation of Latin rectangles and the generation of balanced incomplete block designs. The technique can also be used to perform unbiased statistical analysis, including approximate counting, of sets of objects too large to generate exhaustively.     

Sussmann's orbit theorem and maps

A map between manifolds which matches up families of complete vector fields is a fiber bundle mapping on each orbit of those vector fields.     

Patterned ground formation and convection in porous media with a phase change

The influence of a water-ice phase change on the onset of natural convection is examined for a saturated porous layer overlying a frozen region. Darcy's law is used and a parabolic equation of state is assumed for water. From a linear instability analysis we obtain predictions for the onset of convection in the melted region and the corresponding criticial wavenumber. The critical numbers are calculated by employing finite differences and solving the associated generalized eigenvalue problem. We study the effect varying thermal conductivities and boundary conditions have on these predictions. The analysis is applied to the formation of patterned ground, a geophysical phenomenon of stone borders forming regular hexagonal patterns. The theoretical model for patterned ground is based on natural convection in saturated soil below which is a cold permafrost layer.     

The 3D structure of thuricin CD, a two-component bacteriocin with cysteine sulfur to α-carbon cross-links

Thuricin CD is an antimicrobial factor that consists of two peptides, Trn-α and Trn-β, that exhibit synergistic activity against drug resistant strains of Clostridium difficile. Trn-α and Trn-β each possess three sulfur to α-carbon thioether bridges for which the stereochemistry is unknown. This report presents the three-dimensional solution structures of Trn-α and Trn-β. Structure calculations were performed for the eight possible stereoisomers of each peptide based on the same NMR data. The structure of the stereoisomer that best fit the experimental data was chosen as the representative structure for each peptide. It was determined that Trn-α has L-stereochemistry at Ser21 (α-R), L-stereochemistry at Thr25 (α-R), and D-stereochemistry at Thr28 (α-S) (an LLD isomer). Trn-β was also found to be the LLD isomer, with L-stereochemistry at Thr21 (α-R), L-stereochemistry at Ala25 (α-R), and D-stereochemistry at Tyr28 (α-S).